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Date: 25-1-2021
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Date: 26-1-2021
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A Lehmer number is a number generated by a generalization of a Lucas sequence. Let and be complex numbers with
(1) |
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(2) |
where and are relatively prime nonzero integers and is not a root of unity. Then the corresponding Lehmer numbers are
(3) |
and the companion numbers
(4) |
REFERENCES:
Lehmer, D. H. "An Extended Theory of Lucas' Functions." Ann. Math. 31, 419-448, 1930.
Ribenboim, P. The New Book of Prime Number Records. New York: Springer-Verlag, pp. 61 and 70, 1989.
Shorey, T. N. and Stewart, C. L. "On Divisors of Fermat, Fibonacci, Lucas and Lehmer Numbers, 2." J. London Math. Soc. 23, 17-23, 1981.
Stewart, C. L. "On Divisors of Fermat, Fibonacci, Lucas and Lehmer Numbers." Proc. London Math. Soc. 35, 425-447, 1977.
Williams, H. C. "The Primality of ." Canad. Math. Bull. 15, 585-589, 1972.
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